On dynamics of graph maps with zero topological entropy
| Autor: | Jian Li, Piotr Oprocha, Yini Yang, Tiaoying Zeng |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
37E25
37B40 37B05 Applied Mathematics 010102 general mathematics Null (mathematics) Zero (complex analysis) General Physics and Astronomy Statistical and Nonlinear Physics Topological entropy Dynamical Systems (math.DS) Topological graph Equicontinuity 01 natural sciences 010101 applied mathematics Combinatorics FOS: Mathematics Interval (graph theory) Graph (abstract data type) Equivalence relation Mathematics - Dynamical Systems 0101 mathematics Mathematical Physics Mathematics |
| DOI: | 10.48550/arxiv.1711.01101 |
| Popis: | We explore the dynamics of graph maps with zero topological entropy. It is shown that a continuous map $f$ on a topological graph $G$ has zero topological entropy if and only if it is locally mean equicontinuous, that is the dynamics on each orbit closure is mean equicontinuous. As an application, we show that Sarnak's M\"obius Disjointness Conjecture is true for graph maps with zero topological entropy. We also extend several results known in interval dynamics to graph maps. We show that a graph map has zero topological entropy if and only if there is no $3$-scrambled tuple if and only if the proximal relation is an equivalence relation; a graph map has no scrambled pairs if and only if it is null if and only if it is tame. Comment: 15 pages, updated version, add some references |
| Databáze: | OpenAIRE |
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